Find the Radius of a Circumscribed Circle For a Triangle

Question

The question is the following:

What is the radius of the circumscribed circle for a triangle whose sides are 15, 15, and 24 cm long? What is the radius of the smallest circle that contains this triangle?

I found the height of the triangle to be 9 inches, but I am not sure how to go farther from there. Any help will be greatly appreciated.

Answer 1

HINT:

Since the triangle is obtuse, the radius of the smalles circle is $\frac{1}{2} 24 = 12$

Answer 2

hint...Use the sine rule in the form $$\frac{a}{\sin A}=...=2R$$

So in this case, $$2R=\frac{24}{\sin(2\arcsin(\frac{12}{15}))}$$